I did find in this clause clearly in the New York State regulations:
§160.27 Applicability
Appearance enhancement licensure is not applicable to the following:
(e) Permanent dyeing: No appearance enhancement licensee shall be authorized or permitted to apply dye of any kind to eyelash or eyebrow hair. The link to this is http://www.dos.state.ny.us/lcns/lawbooks/app_enh.html

Looks Like it is a no to me, but please give them a call.
The easiest way to find out is to contact the New York State Board of Cosmetology. Here in Arizona, Lash tinting is legal, however, there are specific products that are ILLEGAL to use. These products contain hydrogen peroxide. The tints we use are all natural based. Your state board will tell you what products you may use near your eyes.